Dimensions and molecular structures play pivotal roles in the principle of heat conduction. The dimensional characteristics of a solution within nanoscale systems depend on the degrees of confinement. However, the influence of such variations on heat transfer remains inadequately understood. Here, we perform quasi-one-dimensional non-equilibrium molecular dynamics simulations to calculate the thermal conductivity of water molecules confined in carbon nanotubes. The structure of water molecules is determined depending on the nanotube radius, forming a single-file, a single-layer, and a double-layer structure, corresponding to an increasing radius order. We reveal that the thermal conductivity of liquid water has a sublinear dependency on nanotube length exclusively when water molecules form a single file. A stronger confinement leads to behavioral and structural characteristics closely resembling a one-dimensional nature. Moreover, single-layer-structured water molecules exhibit enhanced thermal conductivity. We elucidate that this is due to the increase in the local water density and the absence of transitions to another layer, which typically occurs in systems with double-layer water structures within relatively large radius nanotubes.